- Solves expressions and counts the number of significant figures.
- Does not apply the even rule.
- Addition and subtraction round by least number of decimals.
- Multiplication and division round by least number of significant figures.
- Logarithm rounds by the input's number of significant figures as the result's number of decimals.
- Antilogarithm rounds by the power's number of decimals as the result's number of sig figs.
- Exponentiation rounds by the certainty in only the base.
- Rounds on the final step.
- Underlines indicate the least-significant digit in each part of the expression.
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Significant figures (sig figs for short) are the meaningful digits in a number. Often, leading zeroes or trailing zeroes can be removed and the number remains just as accurate (004 means the same as 4, for example).

When removing digits, you must be able to identify the significant figures in order to retain the number’s accuracy. When you round a number up or down, one or some of the significant figures are altered.

**Follow these 3 rules to identify the number of significant figures in a number**: Any digit that is not zero is always significant. Zeroes located between other digits are significant. If there’s a decimal point, then any trailing zeroes are significant.

Let's go through the rules for significant figures in a bit more detail...

**All of the following are significant figures…**

- Any digit that is not 0 is always significant.
- 0 is significant when it’s between other digits, such as 205 or 3.604 (because clearly, 205 is not the same as 25).
- If there’s a decimal point, then any trailing zeroes are significant figures (e.g. 90.7500). These trailing zeroes might seem unnecessary at first glance, but they confirm the precision of the number. 90.75 could well be 90.7511 rounded down to two decimal places. So 90.7500 confirms that it is completely exact to four decimal places.

**And these are not significant figures…**

- Leading zeroes before a non-zero digit are not significant figures (00200 is the same as 200, and 007 is the same as 7, so the leading 0s are not significant. They don’t make the number any more precise).

This principle can be confusing, but leading zeros are still not significant figures, even if they come after a decimal point. 0.01kg of grapes are not the same as 1kg of grapes, so the leading zeroes might seem to be significant. However, 0.01kg can also be expressed as 10g. It’s the same value.

So leading zeroes are not considered to be significant figures; it’s the 1 part that’s significant. Of course, if the zero sits between two significant figures (e.g. 2.303) then the zero is significant, in line with rule (2) explained above. - Trailing zeroes are not significant when there’s no decimal point involved. If there is a decimal point, then, according to rule (3) explained above, any trailing zeroes are considered to be significant figures.

Here are some examples of significant figure calculations:

- 7 has 1 significant figure (7).
- 73 has 2 significant figures (7 and 3).
- 100 has 1 significant figure (1).
- 673 has 3 significant figures (6, 7 and 3).
- 673.52 has 5 significant figures (6, 3, 7, 5 and 2).
- 0.0637 has 3 significant figures (6, 3 and 7).
- 30.00 has 4 significant figures (3, 0, 0 and 0) and 2 decimals.
- 0.0025 has 2 significant figures (2 and 5) and 4 decimals.

You can use the following operators and functions with our calculator:

- Addition ( + ), subtraction ( - ), division ( / or ÷ ) and multiplication ( * or × ). Plus exponent ( ^ )
- Grouping symbols: parentheses ( )
- Functions: log, ln

Our calculator also provides a counter, showing you the number of significant figures for any calculation.

Check out the math calculators at The Calculator Site for assistance with converting decimals to fractions. For those of you at university wanting help with calculating your module, assignment or course grades, give the university grade calculator a try.

- 3.16: Significant Figures. LibreTexts libraries.
- Rules for Significant Figures. Columbia University.